Have you ever been on a road trip with a math teacher? They're always calculating distances and estimating how much farther they can go on a tank of gas and noticing things... This was just what happened during a trip with my wife. We were headed towards the New Brunswick boarder from Halifax and we saw a highway mileage sign. It said it that Amherst was 42 km away and New Brunswick was 47 km away.

"So how far is it from Amherst to New Brunswick?" I asked. 5 km? But is it exactly 5 km? If we assume that these distances are rounded to the nearest kilometer then it might be as far as 6 km (41.5 km to Amherst and 47.4 km to NB) or as short as 4 km (42.4 km to Amherst and 46.5 to NB)? (46.5 - 42.4) <= distance <= (47.4 - 41.5)

A few minutes driving brought us to the next mileage sign and some additional information.

So the next mileage sign down the road seems to indicate that there are only 4 km between Amherst and the NB boarder. Using our previous logic however we could say that it is anywhere between 3 km and 5 km right? (39.5 - 36.4) <= distance <= (40.4 - 35.5). Now we are getting somewhere. We know that it is between 4 and 6 km and between 3 and 5 km.

Now we can narrow it down and say with some certainty that the distance between Amherst and NB was between 4 and 5 km. I'm feeling confident now. A few more kilometers down the road we pass the next mileage sign.

What the what! What is going on here? Is this a conspiracy of cartographers? What strange and inscrutable measurement system is at work here? Time for some Google Earth mapping. I used Google Street View to find the second road sign along the Trans-Canada Hwy 104 where the sign says there is 36 km to Amherst. A straight line from this spot on the road to the geographical centre of Amherst is only about 27 km so I think we can assume that the road signs are measured as the distance along the road.

So lets use Google Maps to measure the distance along the road. From the mileage sign to the city centre, Google Maps says that it is still only about 32 km away. Still about 4 km off what the sign says. I wonder how accurate these signs are? How long ago and using what technology were these signs created?